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Let ${\\bf t}$ denote the Thue-Morse word, and let $\\mathcal F(k)=AP({\\bf t},k)\\cap(2\\mathbb Z^+-1)$. For $k\\geq 3$, $\\gamma(k)=\\min(\\mathcal F(k))$ and $\\Gamma(k)=\\max((2\\mathbb Z^+-1)\\setminus\\mathcal F(k))$ are well-defined odd positive integers. Fici et al. speculated that $\\ga"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1607.05825","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-20T05:07:13Z","cross_cats_sorted":[],"title_canon_sha256":"4b710ecf6fcbbe42fc5d1f45971cbdfdb1fb30ee3eb1d1dadb3d778792d41409","abstract_canon_sha256":"395fc27019e179b910022bf451fd2de91b11d34d58f9e4e852a2dc4cb7783888"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:51.906573Z","signature_b64":"hbZwrBUocVtx/8ApD4HkgKyJh60fyKBAaybP8Gc1EGt6w8nPBbRm7QRGzT3UXr3oVDRi3VnnbdzD4p3GuFklBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2672d13c26e3372f9f93ebd937757f7c4b5e4c556bc37665fc11d533462f5dc","last_reissued_at":"2026-05-18T01:02:51.906111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:51.906111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anti-Power Prefixes of the Thue-Morse Word","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colin Defant","submitted_at":"2016-07-20T05:07:13Z","abstract_excerpt":"Recently, Fici, Restivo, Silva, and Zamboni defined a $k$-anti-power to be a word of the form $w_1w_2\\cdots w_k$, where $w_1,w_2,\\ldots,w_k$ are distinct words of the same length. They defined $AP(x,k)$ to be the set of all positive integers $m$ such that the prefix of length $km$ of the word $x$ is a $k$-anti-power. Let ${\\bf t}$ denote the Thue-Morse word, and let $\\mathcal F(k)=AP({\\bf t},k)\\cap(2\\mathbb Z^+-1)$. For $k\\geq 3$, $\\gamma(k)=\\min(\\mathcal F(k))$ and $\\Gamma(k)=\\max((2\\mathbb Z^+-1)\\setminus\\mathcal F(k))$ are well-defined odd positive integers. Fici et al. speculated that $\\ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05825","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1607.05825","created_at":"2026-05-18T01:02:51.906186+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.05825v3","created_at":"2026-05-18T01:02:51.906186+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.05825","created_at":"2026-05-18T01:02:51.906186+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JTS2E6CNYZX","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JTS2E6CNYZXF6PZ","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JTS2E6C","created_at":"2026-05-18T12:30:01.593930+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01664","citing_title":"On the cyclic regularities of strings","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67","json":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67.json","graph_json":"https://pith.science/api/pith-number/6JTS2E6CNYZXF6PZH26ZG52X67/graph.json","events_json":"https://pith.science/api/pith-number/6JTS2E6CNYZXF6PZH26ZG52X67/events.json","paper":"https://pith.science/paper/6JTS2E6C"},"agent_actions":{"view_html":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67","download_json":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67.json","view_paper":"https://pith.science/paper/6JTS2E6C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.05825&json=true","fetch_graph":"https://pith.science/api/pith-number/6JTS2E6CNYZXF6PZH26ZG52X67/graph.json","fetch_events":"https://pith.science/api/pith-number/6JTS2E6CNYZXF6PZH26ZG52X67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67/action/storage_attestation","attest_author":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67/action/author_attestation","sign_citation":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67/action/citation_signature","submit_replication":"https://pith.science/pith/6JTS2E6CNYZXF6PZH26ZG52X67/action/replication_record"}},"created_at":"2026-05-18T01:02:51.906186+00:00","updated_at":"2026-05-18T01:02:51.906186+00:00"}